How to fill the surface of a "wireframe"-sphere in Blender
You probably have curves. So when converted to mesh, they are disconnected rings or arcs but this is not visible as vertices overlap.

In edit mode: 


select all
remove doubled vertices (you find that in the toolshelf on the left using T to make it appear, or press W to bring up the menu to select it from)
then once all is selected hit F


I confirm this hypothesis after a test on your file.



Concerning the half sphere, same principle but you'll have to remove the unwanted face after that:


Switch to face selection mode CtrlTab, then choose 'face'
Select it RMB
Delete it X then 'only face'